Let Ψ = { ψ 1 , … , ψ L } ⊂ L 2 := L 2 ( − ∞ , ∞ ) \Psi =\{\psi _1, \ldots , \psi _L\}\subset L^2:=L^2(-\infty , \infty ) generate a tight affine frame with dilation factor M M , where 2 ≤ M ∈ Z 2\le M\in \mathbf {Z} , and sampling constant b = 1 b=1 (for the zeroth scale level). Then for 1 ≤ N ∈ Z 1\le N\in \mathbf {Z} , N × N\times oversampling (or oversampling by N N ) means replacing the sampling constant 1 1 by 1 / N 1/N . The Second Oversampling Theorem asserts that N × N\times oversampling of the given tight affine frame generated by Ψ \Psi preserves a tight affine frame, provided that N = N 0 N=N_0 is relatively prime to M M (i.e., g c d ( N 0 , M ) = 1 gcd(N_0,M)=1 ). In this paper, we discuss the preservation of tightness in m N 0 × mN_0\times oversampling, where 1 ≤ m | M 1\le m|M (i.e., 1 ≤ m ≤ M 1\le m\le M and g c d ( m , M ) = m gcd(m,M)=m ). We also show that tight affine frame preservation in m N 0 × mN_0\times oversampling is equivalent to the property of shift-invariance with respect to 1 m N 0 Z \frac {1}{mN_0}\mathbf {Z} of the affine frame operator Q 0 , N 0 Q_{0,N_0} defined on the zeroth scale level.